In nuclear medicine, the collimator performs the essential function of focusing gamma-rays. Radioactive tracers are injected into a patient for the determination of physiological functions within the body. The gamma- ray emissions from these radionuclides are detected by gamma-ray cameras that produce images of the activity distribution in the patient. The focusing results from the passive absorption of the radiation within the collimator. If a gamma-ray strikes the absorbing material in the collimator septa, it is generally absorbed with minimal penetration. Most clinical collimators currently have parallel holes. For these collimators, a well-known trade-off exists between sensitivity (the fraction of the emitted gamma-rays that are detected) and the resolution (the ability to distinguish between two sources located close to one another). One can increase sensitivity only by sacrificing resolution. During the past few decades, significant effort has produced parallel-hole collimators with close to optimal performance; that is, these collimators produce the greatest sensitivity possible for a particular resolution. Nonetheless, the sensitivity of collimators in nuclear medicine is so low that most clinical images display significant statistical noise. Converging-hole collimators now are considered the best means of increasing the sensitivity of gamma-ray cameras. Commercial vendors have begun producing fanbeam and conebeam collimators that produce images by aligning the collimator holes toward an axis or a focal point. Unfortunately, the design of converging- hole collimators is more difficult than the design of parallel-hole collimators. Not only is the geometry more complicated, but the evaluation of septal penetration and hole-pattern effects are more difficult. In the proposed research, the imaging properties of converging- and tapered-hole collimators will be evaluated by computer simulations. Ray-tracing techniques will be used to calculate the geometric and penetration response. For converging-hole collimators, a three-dimensional tracing program is required. Each hole in a converging-hole collimator may have a different axis and taper. Because a typical collimator may have 105 hole positions, axes, and tapers must be specified algorithmically from a limited set of parameters (e.g., collimator thickness, focal length, etc.). Furthermore, the method of collimator scaling will be used; so that, geometrically similar collimators can be evaluated without repeating the ray-tracing process. The simulations will be tested by comparison with existing ray-tracing programs in the limiting case of parallel-hole designs and with experimental measurements on existing fanbeam and conebeam collimators. Following verification, the programs will be used for the evaluation of collimator designs over a wide range of design parameters. In particular, we will determine an empirical criterion that will permit systematic optimization of collimator designs.